Role of nuclear tunneling in aqueous ferrous–ferric electron transfer

By computer simulation and also by analytical methods we have computed the nuclear tunneling enhancement of the rate for ferrous–ferric exchange in water. The model we have examined is the one studied earlier where we treated water as a classical liquid R. A. Kuharski, J. S. Bader, D. Chandler, M. Sprik, M. L. Klein, and R. W. Impey, J. Chem. Phys. 89, 3248 (1988). But now we treat water quantum mechanically and find that the tunneling enhancement is a factor of 60 in the rate constant. Further, as observed experimentally, we find that the isotope shift on the rate when changing from D2O to H2O is approximately a factor of 2. The computer simulation aspects of these calculations employ path integral methods and a novel partitioning of the free energy associated with electron transfer. Our results show that it is insufficient to quantize only the atoms composing the ligands. The quantum dynamics of water molecules beyond the first solvation shell prove quite significant.